Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
268 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×C4×#733 | C2 | semidirect |
| 3. Dic3×#733 | C2 | semidirect |
| 8. D3×#733 | C4 | direct (N × H) |
| 19. C4×#733 | D3 | direct (N × H) |
| 20. C3×#733 | C2×C4 | semidirect |
| 57. #733 | C4×D3 | direct (N × H) |
| 107. C4×D3 | #733 | direct (N × H) |
| 130. C3×C4 | C2×#733 | semidirect |
| 132. Dic3 | C2×#733 | semidirect |
| 150. D3 | C4×#733 | direct (N × H) |
| 153. C4 | D3×#733 | direct (N × H) |
| 157. C3 | C2×C4×#733 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×#733 | 2 |
| C3×C4×#733 | 2 |
| Dic3×#733 | 2 |
| C4×D3×3−1+2 | 3 |
| C3×C4×D3×C9 | 3 |
| C2×C4×#733 | 3 |